This paper is devoted to both theoretical and numerical study of Riccati equation with fractional order. A formulation to the fractional-order Legendre operational matrix of fractional integration is constructed. Existence and uniqueness results for the considered problem are provided and proved. The fractional derivative is described in the Caputo sense. Some numerical examples are discussed to demonstrate the efficiency and the accuracy of the proposed algorithm.
- Fractional-order Legendre function
- Operational matrix of fractional integration
- Riccati equation with fractional order
ASJC Scopus subject areas
- Computational Mathematics
- Applied Mathematics